Controlled state reconstruction and quantum secret sharing
Pahulpreet Singh, Indranil Chakrabarty
Abstract
In this article we present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing for general three-qubit states. This is achieved by providing a closed expression for the reconstruction fidelity, which relies on the genuine tripartite correlation and the bipartite channel between the dealer and the reconstructor characterized by the respective correlation parameters. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at $\frac{2}{3}$. This article introduces new interoperability between teleportation and state reconstruction. This is detailed through a case-by-case analysis of relevant correlation matrices. We reformulate the idea of quantum secret sharing by setting up additional constraints on the teleportation capacity of the bipartite channels between dealer and shareholders by ensuring that, individually, the shareholders cannot reconstruct the secret. We believe that this will give us an ideal picture of how quantum secret sharing should be.